The Percent Change Formula, Explained Simply

Percent change describes the size of a jump or a drop relative to where something started. A raw difference like "up by 20" does not mean much on its own, because 20 added to 40 is huge while 20 added to 4,000 is tiny. Turning that difference into a percentage gives you a fair, comparable number no matter the starting scale, which is exactly why it shows up in finance, science, grades, and everyday shopping. If you are brand new to percentages in general, skim our guide on how to calculate a percentage first, then come back here for the change-over-time version.

What is the percent change formula?

Here is the whole thing in one line. Subtract the old value from the new value, divide that difference by the old value, then multiply by 100 to convert it into a percentage.

The single most important detail is the denominator. You divide by the old value, the number you started from, because percent change always answers the question "how big was this move compared to where we began." Dividing by the new value instead is the most common error people make, and it quietly produces the wrong answer every time. Think of the old value as your baseline, the yardstick every move is measured against.

The multiply-by-100 step is just unit conversion. Divide 20 by 80 and you get 0.25, which is the change written as a decimal fraction of the original. Multiplying by 100 restates that same 0.25 as "25 per hundred," which is what the word percent literally means. If you ever only need the ratio, stop at 0.25; if you need the percentage, finish the multiply.

Is the result an increase or a decrease?

The formula handles direction for you automatically through its sign. You do not need a separate rule for increases and decreases, the subtraction does the work:

• Positive result: the value went up. A result of plus 25 means a 25 percent increase.
• Negative result: the value went down. A result of minus 25 means a 25 percent decrease.
• Zero: nothing changed. The new and old values are equal.

Because the sign already tells you the direction, you usually report the percentage as a plain positive number and describe it with words: "a 25 percent increase" or "a 25 percent decrease." The math is identical either way. Some people prefer to memorise two separate versions of the formula, and that is fine too: for a rise, (new minus old) / old times 100, and for a fall, (old minus new) / old times 100 to get a positive figure. Both are the same rule seen from different ends.

How do you calculate percent change? A worked example

Suppose a jacket was priced at 80 dollars last month and is now 100 dollars. What is the percent change in price? Work through it one line at a time so the method sticks.

1. Identify the old value and the new value. Old equals 80, new equals 100.
2. Subtract: 100 minus 80 equals 20. That is the raw difference.
3. Divide by the old value: 20 divided by 80 equals 0.25.
4. Multiply by 100: 0.25 times 100 equals 25.
5. Read the sign: the result is positive, so the price rose by 25 percent.

Now reverse it. The jacket goes back from 100 dollars to 80 dollars. The difference is 80 minus 100 equals minus 20, divided by the old value of 100 equals minus 0.2, times 100 equals minus 20. So it is a 20 percent decrease. Notice that the same two prices give a 25 percent rise one way and a 20 percent fall the other way. That is not a mistake. The starting point changed, so the base you divide by changed too. This single fact is the source of most confusion about percentages, and once it clicks the rest is easy.

Percent change quick reference chart

Use this table to sanity check your own calculations. Every row starts from an old value of 100 so the pattern is easy to see, but the same percentages hold for any starting number. If your old value is not 100, the shape of the result is identical, only the base changes.

Notice that doubling a value is a 100 percent increase, while losing half of it is only a 50 percent decrease. The asymmetry trips people up, but it follows directly from always dividing by the original value. A move all the way down to zero is a 100 percent decrease, the largest drop possible, but there is no ceiling on the increase side: a value can grow by 300 or 1,000 percent and beyond.

How do you find percent change in Excel or Google Sheets?

Spreadsheets make percent change a one-cell job. Put the old value in cell A2 and the new value in B2, then in C2 enter the formula =(B2-A2)/A2 and format the cell as a percentage. The formula follows the exact same rule as the pencil-and-paper method: new minus old, divided by old. Formatting as a percentage applies the times-100 step for you, so you do not multiply by 100 yourself.

• Increase or decrease shows automatically. A positive cell is a rise, a red or negative cell is a fall, just like the sign in the formula.
• Guard against a zero baseline. If the old value can be 0, wrap it as =IF(A2=0,"n/a",(B2-A2)/A2) so the sheet does not throw a divide-by-zero error.
• Copy down a column to compare a whole list of before-and-after pairs at once, which is where spreadsheets beat a calculator.

Where percent change shows up in real life

• Money and prices: a stock that moves from 40 to 46 is up 15 percent, and a discount works the same way in reverse. Our discount calculator uses this exact logic.
• Salary and income: a raise from 50,000 to 53,000 is a 6 percent increase.
• Inflation and economics: statistical agencies report inflation as a percent change. The US Bureau of Labor Statistics publishes it as the 12-month percent change in the Consumer Price Index, which is percent change applied to price data over time.
• Grades and test scores: going from 70 to 84 on two exams is a 20 percent improvement.

Percent change is closely related to a few other formulas, and knowing which one you need matters. If you are comparing a measured value against a known true value rather than tracking a value over time, you want percent error instead. If you are specifically measuring a rise, our step-by-step guide to percentage increase walks through it in detail. And if you are watching something grow repeatedly at the same rate, compound interest takes percent change and applies it again and again.

Common mistakes to avoid

• Dividing by the new value. Always divide by the old, original value. Using the new value gives a different, incorrect answer.
• Mixing up which number is old. Whichever value came first in time is the old value, even if it is larger than the new one.
• Forgetting the multiply by 100. Skipping it leaves you with a decimal like 0.25 instead of 25 percent.
• Confusing percent change with percentage points. Going from 10 percent to 15 percent is a 5 percentage point rise, but a 50 percent change. They are not the same thing.
• Dropping the sign too early. Keep the negative sign until the end so you know whether it is an increase or a decrease.
• Assuming increases and decreases cancel. A 50 percent rise followed by a 50 percent fall does not return you to the start, because the second percentage is taken from a bigger base.

Good to know: edge cases and gotchas

If your old value is zero, percent change is undefined, because you cannot divide by zero. There is no meaningful percentage jump "from nothing," so report the raw change instead. The same care applies when the old value is negative, such as a temperature or a bank balance below zero: the formula still runs, but the sign of the result can be counterintuitive, so state the actual before-and-after numbers alongside the percentage to avoid confusion.

Remember too that percent change is not reversible. A 50 percent increase followed by a 50 percent decrease does not return you to the start, since the second percentage is taken from a larger base. Starting at 100, a 50 percent rise gives 150, and a 50 percent fall from 150 removes 75, leaving you at 75. To undo a 50 percent increase exactly, you actually need a decrease of about 33 percent.

Percent change tells you the size of a move relative to where it began. Change the starting point and you change the percentage.

Skip the arithmetic. Enter your old value and new value below and the calculator returns the percent change, ready to read off with the correct sign.

Once the formula clicks, percent change becomes one of the most useful tools you own for making sense of numbers that move. Master the rule "subtract, divide by the old value, multiply by 100" and you can compare almost any before and after with confidence.